Lecture Event
"Closed holomorphic differentials and holomorphic webs"
Prof. Dr. Fedor Bogomolov
2 Aug 2010, 16:15 – 17:15
FU (Arnimallee 3, Raum 119)
I will report on a progress in our joint work with Bruno de Oliveira.
We call a symmetric holomorphic differential $s$ on a complex manifold closed if it can be written as $\prod df_i^{n_i}$ in the local neighborhood of some point $x_o$ of the manifold.
This property helds then for a complementary of a finite set of divisors and hence such a differential defines a holomorphic web- a set of local codimension one foliations on the manifold ( possibly singular).
Note that any symmetric differential on surface defines a similar web.However the webs defined by closed differentials are very special and provide with restrictions on the tolology of the ambient surface ( or manifold). I will discuss some results and conjectures.
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